Lesson 5, Topic 1
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# Meaning of Work, Energy and Power

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### Work:

Work can be defined as the product of force and distance through which an object moves in the direction of force applied.

Work (W) = Force (F) x distance (D)

= Newton x metre

= Joule (J)

Where Force is the product of mass and gravity or mass and acceleration (F = mg, or F = ma) (g = 10m/s2)

The unit of work is Joule named after the scientist, James Prescott Joule, who did a lot of experiments with energy.

Example 1

If a force of 20 N is used to pull a Wheelbarrow through a distance of 8 m. How much work is done in the process.

Solution

Work done = Force x Distance

Work done = $$\scriptsize 20 N \: \times \: 8 \\ \scriptsize = 160 J$$

Example 2

A boy of mass 50kg runs up a staircase through a distance of 15m. Calculate the work done by the boy.

(Take g = 10m/s2)

Solution

mass of the boy = 50kg, Distance = 15m, g = 10 m/s2

Force = mass x gravity

Force = $$\scriptsize 50\:kg \: \times \: 10m/s^2 \\ \scriptsize = 500 \:N$$

Work done = $$\scriptsize Force \: \times \: Distance \\ \scriptsize = 500\:N \: \times \: 15\:m \\ \scriptsize = 7500\:J$$

1000 Joules (J) =1 Kilojoules (KJ)

Therefore,

7500 Joules (J) = 7.5 Kilojoules (KJ)

### Energy:

Energy may be defined as the ability to do work. It can be transferred from one object to another by doing work. Anything that is capable of doing work has energy. Energy is also measured in joules. The main source of energy is the sun.

### Power:

Power is defined as the rate at which work is done. Power is the amount of work done divided by the time taken to do it.

Power is expressed as   P =  $$\frac{W}{T}$$

Where W = Work done and T = time taken.

Power = $$\frac{Work\: done}{Time} \\ = \frac{Force \: \times \: Distance}{Time}$$

The S.I unit of power is Joules per second or Watt (W).

Larger units are Kilowatt (KW) and megawatt (MW)

1KW = 1000W

1MW = 1 million Watts or 106 W

Example 3

A gymnast lifts a mass of 85 kg vertically through a height of 5 m in 3 seconds. Calculate the power developed.

(Take g = 10m/s2)

Solution

mass = 85 kg, distance = 5m, time = 3 s

Power = $$\frac{Work\: done}{Time} \\ = \frac{Force \: \times \: Distance}{Time}$$

Force = $$\scriptsize mass \: \times \: gravity \\ \scriptsize = 85 \: \times 5 \\ \scriptsize = 425\: N$$

Work = $$\scriptsize Force \: \times \: Distance \\ \scriptsize = 425 \: \times \: 5 \\ \scriptsize = 2125\:J$$

Power = $$\frac{2125}{3} \\ \scriptsize = 708.33 \: W$$

Example 4

A motorcycle travelling at 30 m/s moves with a force of 650 N. What is the Power produced?

Power = $$\frac{Work\: done}{Time} \\ = \frac{Force \: \times \: Distance}{Time} \\ = \scriptsize Force \: \times \: \normalsize \frac{distance}{time}$$
But $$\frac{distance}{time} \\ \scriptsize = velocity$$
P = $$\scriptsize F \: \times \: V \\ \scriptsize = 650 \: \times \: 30 \\ \scriptsize = 19500 \: W \\ \scriptsize = \normalsize \frac{19500}{1000} \: \scriptsize KW \\ \scriptsize = 19.5 \: KW$$